Problem: Simplify the following expression: $r = \dfrac{-4z}{2z} - \dfrac{-7z - 11}{2z}$
Since the expressions have the same denominator we simply subtract the numerators: $r = \dfrac{-4z - (-7z - 11)}{2z}$ Distribute the negative sign: $r = \dfrac{-4z + 7z + 11}{2z}$ Combine like terms: $r = \dfrac{3z + 11}{2z}$